You awaken on a deep space observing station. You do not know its acceleration history but right now there is no gravity and you are billions of light years from the nearest other molecules. A light-year-long series of high speed, high resolution video cameras stretches out left to right as viewed from your observation deck. Each camera has a big LED clock attached to it, which is kept in sync with the clock in your observation post, and which appears in the foreground of every picture. Also there is a yardstick next to each camera so passing observers can measure relative speed.
Your friend awakens aboard a 40m-long spaceship that’s adrift in deep space. He has no memory. After awhile his ship happens to drift in a line exactly parallel to your cameras. His ship has a big LED clock on the side that your cameras can see. His ship itself also has a high-speed camera aboard that records pictures of your cameras’ clocks each time it passes one, and in the foreground of its pictures, the clock attached to his ship is also visible.
Neither of you can ever remember having experienced gravity or acceleration, so it is unknown which of you is the one who accelerated to achieve the speed difference. It’s entirely possible you both accelerated the same amount in opposite directions. Who knows.
From your observation deck, after 1.001001001001001 years, your friend’s ship finally passes the last camera. Upon observing the complete set of photos, you see that your clock and his ship’s clock were exactly in sync in the first photo taken when he initially passed your first camera. Due to the elapsed time, you calculate his velocity was 0.999x the speed of light. Due to time dilation, the clock on the exterior of his ship has only elapsed 16 days, 8 hours, 3 minutes from the first picture you took. Also, his ship only appears to be 1.7884 m in length—4.4471% of the original length.
Meanwhile, your friend’s ship’s clock has also taken photos of your cameras’ clocks as they whizzed past. Finally, there was a quick wifi transmission between his clock and your final clock, over which connection, the final photographs were exchanged.
To him, how far would your line of clocks appear to stretch? I calculate 0.044515 LY, due to your length contracting relative to him.
Since you are moving 0.999 c relative to him, I calculate that he would only experience 16 days, 8 hours, 3 minutes having passed while your line of cameras zipped past him. Is this correct? If so, why does he experience a different amount of elapsed time compared to you?
If I’m right then the photo of his own ship that he receives from your final camera will show 16 days, 8 hours, 3 minutes as having elapsed on the outside clock of his ship while your camera’s own foreground clock will indicate 1.001001... years as having passed. Is that what would happen, no matter who was the one that accelerated? Or does some acceleration that occurred in the past affect things? If so, why?
Lastly, the final picture you receive from him would show the same elapsed times as the picture he received from you: his ship has 16 days, 8 hours, 3 minutes, and your final clock has 1.001... years in both pictures. Correct?
If I’m correct on the above points, then I am confused, because it seems asymmetrical.
I would have expected that if you saw his clock elapsed by 16 days, 8 hours, 3 minutes while you experienced 1.001... years, then likewise, he would see:
- your final clock shows 16 days, 8 hours, 3 minutes passed for you
- his clock shows a year had passed for him
- his own calculation of your velocity, using the shrunken yardsticks next to your cameras as a guide, would be 0.999c
However in this scenario, would either of you receive the wifi data exchange? Your final clock would send it after 1.001... years, but to him, your final clock only shows 16 days 8 hours 3 minutes have passed—so how can he be receiving a file that your clock only sends after 1.001... years?